Chapter 8.2, Problem 35PPS

To determine

To solve the given equation.

Answer to Problem 35PPS

  $f=0.69$

Explanation of Solution

Given:

  $2f\left(5f-2\right)-10\left(f^2-3f+6\right)=-8f\left(f+4\right)+4\left(2f^2-7f\right)$

Calculation:

Solving the given equation,

  $\Rightarrow 2f\left(5f-2\right)-10\left(f^2-3f+6\right)=-8f\left(f+4\right)+4\left(2f^2-7f\right)$

  $\Rightarrow 10f^2-4f-10f^2+30f-60=-8f^2-32f+8f^2-28f$   [Solving the brackets]

  $\Rightarrow 10f^2-10f^2-4f+30f-60=-8f^2+8f^2-32f-28f$   [Rearranging the terms]

  $\Rightarrow 26f-60=-60f$  [Solving both sides]

  $\Rightarrow 26f-60+60f=0$  [Solving both sides]

  $\Rightarrow 26f+60f-60=0$  [Rearranging the terms]

  $\Rightarrow 86f-60=0$

  $\begin{array}{l}\Rightarrow 86f=60\\ \Rightarrow f=\frac{60}{86}\\ \Rightarrow f=\frac{30}{43}\\ \Rightarrow f=0.69\end{array}$

Conclusion:

Therefore, the value of $f=0.69$ .